User blog:GamesFan2000/GamesFan's Array Function
I've known about this wiki for quite a while, and as a person who loves math, the stuff featured here is very interesting. So, I decided to try my hand at making a googological function. It's a unique form of array notation that I have theory crafted over the past few weeks with different rules and symbols. The language used in it is quite simple, and some of the definitions might not be obvious unless you apply earlier rules or are good at understanding ambiguity. I also do not have a good understanding of the fast-growing hierarchy or related ordinal-based functions, so I won't be providing comparisons. This is my array notation, which you can call GamesFan's array notation, but I've called it Explosively-Powerful Array Notation, or EPAN. I'd like to see someone solve the growth of this function. Linear Arrays Part 1: Single-entry and Two-entry arrays (a) = a (a, b) = a>a>a...>a, or a b-length arrow chain of a's Part 2: Three-entry arrays and beyond (a, b, c) = ((a, b, c-1), (a, b, c-1), c-1) = (((a, b, c-2), (a, b, c-2), c-2), ((a, b, c-2), (a, b, c-2), c-2), c-1) Subtract one from the last entry, replace a and b with new arrays, make c-1 the last entry and (a, b, c-1) the other entries. Then, do not subtract again from the last entry in the main array yet, but instead subtract from the last entries within the contained arrays and replace a and b in those arrays with (a, b, c-2). Repeat with this logic until c = 0 in the most contained arrays, then solve until the most contained arrays are three-entries long, then refer back to how the subtraction of c and array decomp works. Repeat until c = 0 in the main array and then either solve, or, for four-entries or longer, move on to the next-last entry and repeat this logic until completion. A(n) = (n, n, n, n, n, n, n…, n), or an n-length array of n-valued entries Planar Arrays Part 1: Condensed Linear Arrays (a(b)c) = An array of a’s with a length equal to a solved (c, b)-length array of b's (a(b)c(d)e) = An array of c's with a length equal to a solved (e, d)-length array of d's, then an array of a's with a length equal to a solved ((c, c..., c), b)-array of b's Part 2: Dimensional Arrays (a (b, c) d) = An array of a's with length equal to a solved (d, c, b)-length array of (d, c)-length arrays of (d, b)-length arrays of (c, b)-length arrays of b's (a (b, c) d (e, f) g) follows the same rules as (a(b)c(d)e) Part 3: Super-dimensional Arrays (a (b, c, d) e) = An array of a's with a length equal to a solved (e, d, c, b)-length array (e, d, c)-length arrays of (e, d, b)-length arrays of (e, c, b)-length arrays of (d, c, b)-length arrays of (e, d)-length arrays of (e, c)-length arrays of (e, b)-length arrays of (d, c)-length arrays of (d, b)-length arrays of (c, b)-length arrays of b's AP(n) = (n, n, n, n…, n (n, n, n, n…, n) n, n, n, n…, n (n, n, n, n…, n) …, n), or an n-length series of n-length planar definitions applied to n-length arrays, all with entries of n-value Cuboidal Arrays (abc) follows the same rules as the planars, but it affects the length of the planar definers in addition to the length of the outside arrays ACu(n) applies the same logic to cuboidal arrays as AP(n) does to planar arrays All array levels beyond cuboidal use the same rules in relation to the lower level as cuboidals do in relation to planars To go beyond cuboidal, add another set of square brackets around the definer space Hyper-Condensed Arrays (a{b}c) = An array of a's in a level equal to a solved (c, b)-length array of b's and in a series of a length equal to a (c, b)-length array of b's with individual arrays and definer-arrays equal to a solved (c, b)-length array of b's If more than one curly bracket set is around the definers, then you are to repeat the process in a series of a length equal to a solved (c, b)-length array of b's in the next hyper-level down, with individual arrays of a's with a length equal to a solved (c, b)-length array of b's. (Specific to the example, use the rules defined in the planars to solve) Black Hole Arrays (a/b\c) uses the same rules in relation to hyper-condensed arrays as the hyper-condensed arrays use in relation to the condensed arrays All forms of this notation can be combined together, using their respective rules to solve The final function for this notation is EPAN(n), or F(n), which means that you have to apply n to every variable possible within this notation. You can also use arrays within each function, whether or not it follows my system or another system, but the number must be solved in my notation after the initial array is solved. Category:Blog posts